Introduction To Circuit Analysis Laboratory Lab Experiment 7

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Student's Name:Date:Introduction to Circuit Analysis LaboratoryLab Experiment7Series-Parallel Circuits and In-circuitresistance measurementSeries-Parallel CircuitsMost practical circuits in electronics are made up combinations of both series and parallel circuits.These circuits are made up of all sorts of components such as resistors, capacitors, inductors,diodes, transistors and integrated circuits. Such a circuit, where the components are not strictly inseries or in parallel, is called series-parallel circuit. There is no real world application for a seriesparallel circuit made up of only resistors. In this lab however, we investigate series-parallel circuitsmade up of only resistors to learn about such circuits. The concepts we investigate here can thenbe applied to real world circuits. In this experiment, we will investigate a series-parallel circuit.The voltages and the currents in the circuit will be measured and then compared to the expectedvalues.Remember that you can only combine resistors that are in series or resistors that are in parallel.Series resistors add. Resistors in parallel can be combined using either the conductance method orthe “product over sum” method (two resistors at a time). The conductance method, you remember,is easier to use with the calculator. Two resistors may be recognized to be in series if they haveone node in common and nothing else is connected to that node, it means that the node has a degreeof two. Resistors may be recognized to be in parallel, if they are connected between the same twonodes. If two resistors are neither in series nor in parallel, they cannot be combined. Only resistorsin series or in parallel can be combined.Circuit 7.1 shows a series-parallel circuit. Note that R1 cannot be combined with either R2 or R3;R1 is neither in series nor in parallel with either R2. However, R2 is in parallel with R3, because theyare connected between the same two nodes (node B and ground).Lab 7: Series-Parallel Circuit- Introduction to Circuit Analysis Laboratory Experiment - Page 1 of 11

Circuit 7.1 Series-Parallel Resistivity CircuitThe equivalent combination of R2//R3 is easily found by using the equation the reciprocal of totalconductance formula𝑅2 𝑅3 111(𝑅 𝑅 )23 111(330Ω 680Ω) 222ΩYou can also use the special formula, product over the sum, for two resistors connected inparallel𝑅2 𝑅3 (𝑅2 𝑅3 ) (330Ω 680Ω) 222Ω(𝑅2 𝑅3 ) (330Ω 680Ω)This parallel combination can now be seen to be in series with the 100 resistor R1.Circuit 7.1A – Equivalent Circuit from Circuit 7.1 (R2 R3)Lab 7: Series-Parallel Circuit- Introduction to Circuit Analysis Laboratory Experiment - Page 2 of 11

The total resistance can be calculates as follows:RT R1 ( R2 // R3 ) 100 222 322 The 9V power supply therefore “sees” 322 . Ohm’s Law allows us to predict the total current.IT VT9 0.028A 28mART 322About the current distribution in Circuit 7.1, you can note since the positive of the voltage sourceis connected in series with R1, the current through R1 is the same as the voltage source. At nodeB, the current source or current coming out from R1 divides in two path. Check Circuit 7.2 forreference.Circuit 7.2 – Current distribution for Circuit 𝒗𝒂𝒍𝒖𝒆 𝑴𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝒗𝒂𝒍𝒖𝒆% 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 () 𝒗𝒂𝒍𝒖𝒆Formula 7.1 – Percentage of difference formulaLab 7: Series-Parallel Circuit- Introduction to Circuit Analysis Laboratory Experiment - Page 3 of 11

Laboratory ExperimentPart 1 – Resistance Measurement in a Series-Parallel Circuit1. Obtain a protoboard, jumper wires, and 100 Ω, 330 Ω, and 680 Ω resistors from yourcomponent kit. Measure each resistor separately and record measurement in Table 7.1.Actual resistanceMeasured resistance% of differenceR1 100 ΩR2 330 ΩR3 680 ΩTable 7.1 – Individual resistance measurement2. Build Circuit 7.1 into your protoboard, but don’t make the connection to voltage sourceyet.3. Measure total resistance of Circuit 7.1 as shown in Figure 7.1. Record your measurementin Table 7.2. Do not forget the unit.Figure 7.1 – Total resistance measurement using a DMM4. Calculate the total resistance and the percentage of difference between your calculatedand measured total resistance and record your result in Table 7.2Calculated RTMeasured RT% of differenceTotal ResistanceRTTable 7.2 – Total Resistance Analysis in a Series-Parallel Circuit, Circuit 7.1Lab 7: Series-Parallel Circuit- Introduction to Circuit Analysis Laboratory Experiment - Page 4 of 11

Show calculations of total resistance here:Part 2 – Current Analysis in a Series-Parallel Circuit5. Turn ON the power supply and it to 9 V. Connect the power supply in Figure 7.1 topower and complete Circuit 7.16. Set up the DMM and Circuit 7.1 to measure current. Remember to break one terminalopen of the element to be measured and place the DMM in series or between the openterminals.7. Measure the current through each element in Circuit 7.1 and record the measurements inTable 7.3. Remember that you MUST turn OFF or disconnected the power supply firstbefore making changes to the circuit.8. Calculate the current through each resistor and voltage source in Circuit 7.1. Recordcalculation in Table 7.3.Show calculations of current through each resistor and voltage source here:9. Find the percentage of difference between the measured and calculated current. Recordthe result in Table 7.3.Lab 7: Series-Parallel Circuit- Introduction to Circuit Analysis Laboratory Experiment - Page 5 of 11

Current throughvoltage source, IsCurrent Through Current Through Current ThroughR1 100 R2 330 R3 680 Does KCLHold? le 7.3 Current Analysis in a Series-Parallel Circuit, Circuit 7.1Part 3 – Voltage Analysis in a Series-Parallel Circuit10. Set the DMM and Circuit 7.1 to measure voltage.11. Measure the voltage across each resistor and voltage source. Record the measured valuein Table 7.4.12. Calculate the voltage across each resistor and voltage source in Circuit 7.1. Recordcalculation in Table 7.4.Show calculations of voltage across each resistor here:13. Find the percentage of difference between the measured and calculated voltage. Recordthe result in Table 7.4.14. Turn OFF the power supply, disassemble the circuit and place your component in theirrespective kit. Proceed with Circuit 7.2Lab 7: Series-Parallel Circuit- Introduction to Circuit Analysis Laboratory Experiment - Page 6 of 11

VoltageSource, VsVoltage acrossR1 100 Voltage acrossR2 330 Voltage acrossR3 680 Does KVLHold? le 7.4 Voltage Analysis in a Series-Parallel Circuit, Circuit 7.1Part 4 – Resistance, Voltage, and Current Analysis in a Series-ParallelCircuitCircuit 7.2 – Series-Parallel Resistivity Circuit15. Obtain resistors: 100 Ω, 330 Ω, 220 Ω, and 470 Ω. Measure each resistor separately andrecord measurement in Table 7.5.Actual resistanceMeasured resistance% of differenceR1 100 ΩR2 330 ΩR3 220 ΩR4 470 ΩTable 7.5 – Individual resistance measurementLab 7: Series-Parallel Circuit- Introduction to Circuit Analysis Laboratory Experiment - Page 7 of 11

16. Build Circuit 7.2 into your protoboard, but do not make the connection to voltage sourceyet.17. Measure total resistance for Circuit 7.2. Record your measurement in Table 7.6. Do notforget to include the unit.18. Calculate the total resistance for Circuit 7.2 and record the calculated total resistance inTable 7.6Show calculations of total resistance here:Calculated RTMeasured RT% differenceTotal Resistance, RTTable 7.6 – Total Resistance Analysis in a Series-Parallel Circuit, Circuit 7.2Part 5 - Current Analysis in a Series-Parallel Circuit19. Calculate the current through each resistor and voltage source in Circuit 7.3. Recordcalculation in Table 7.7.Lab 7: Series-Parallel Circuit- Introduction to Circuit Analysis Laboratory Experiment - Page 8 of 11

Show calculations here:20. Turn ON the power supply and set it to 9 V. Connect the power supply to completeCircuit 7.221. Set the DMM and prepare Circuit 7.2 to measure current. Remember to break oneterminal open of the element to be measured and place the DMM in series or between theopen terminals.22. Measure the current through each element in Circuit 7.2 and record the measured value inTable 7.7. Remember that you MUST turn OFF or disconnected the power supply firstbefore making changes to the circuit.23. Find the percentage of difference between the measured and calculated current. Recordthe result in Table 7.7.Current throughvoltage source, IsCurrent ThroughR1 100 Current ThroughR2 330 Current ThroughR3 220 Current ThroughR4 470 MeasuredValueCalculatedValue%DifferenceTable 7.7 Current Analysis in a Series-Parallel Circuit, Circuit 7.2Lab 7: Series-Parallel Circuit- Introduction to Circuit Analysis Laboratory Experiment - Page 9 of 11

Part 6 - Voltage Analysis in a Series-Parallel Circuit24. Calculate the voltage across each resistor and voltage source in Circuit 7.2. Recordcalculation in Table 7.8Show calculations here:25. Set DMM and prepare Circuit 7.2 to measure voltage.26. Measure the voltage across each resistor and voltage source. Record the measured valuein Table 7.827. Find the percentage of difference between the measured and calculated voltage. Recordthe result in Table 7.8VoltageSource, VsVoltage acrossR1 100 Voltage acrossR2 330 Voltage acrossR3 220 Voltage acrossR4 470 MeasuredValueCalculatedValue%DifferenceTable 7.8 Voltage Analysis in a Series-Parallel Circuit, Circuit 7.228. Turn OFF the power supply, disassemble the circuit and place your component in theirrespective kit.Lab 7: Series-Parallel Circuit- Introduction to Circuit Analysis Laboratory Experiment - Page 10 of 11

Questions1. A student built Circuit 7.1 and measured the voltage through each resistor. The studentmeasured 9 V for all three resistors. What was the mistake that the student made?Explain your answer.2. A student built Circuit 7.2 and measured the total resistance using a DMM. The recordedtotal resistance was around 101 Ω. What was the mistake that the student made? Whatshould the student do to measure total resistance correctly? Explain your answer.3. For Circuit 7.2, if a student measured the current through R1, R2, and R3 and found thatthey were the same current. Just by observation, how can you justify that the measuredcurrents are wrong?Answers:Student’s Signature:Lab Instructor’s -- LAB EXPERIMENT ENDS HERE --------------------------------------Lab 7: Series-Parallel Circuit- Introduction to Circuit Analysis Laboratory Experiment - Page 11 of 11

Lab Experiment 7 Series-Parallel Circuits and In-circuit resistance measurement Series-Parallel Circuits Most practical circuits in electronics are made up combinations of both series and parallel circuits. These circuits are made up of all sorts of components such as resistors, capacitors, inductors, diodes, transistors and integrated circuits.

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